Simplify the following expression: $ x = \dfrac{7k}{k - 4} - \dfrac{1}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{7k}{k - 4} \times \dfrac{2}{2} = \dfrac{14k}{2k - 8} $ Multiply the second expression by $\dfrac{k - 4}{k - 4}$ $ \dfrac{1}{2} \times \dfrac{k - 4}{k - 4} = \dfrac{k - 4}{2k - 8} $ Therefore $ x = \dfrac{14k}{2k - 8} - \dfrac{k - 4}{2k - 8} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{14k - (k - 4) }{2k - 8} $ Distribute the negative sign: $x = \dfrac{14k - k + 4}{2k - 8}$ $x = \dfrac{13k + 4}{2k - 8}$